CN113759706B - Multi-rotor attitude active disturbance rejection control method and system based on axial angle vector - Google Patents
Multi-rotor attitude active disturbance rejection control method and system based on axial angle vector Download PDFInfo
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Abstract
The invention relates to a multi-rotor attitude active disturbance rejection control method and a system based on an axial angle vector, which comprises the following steps: acquiring three-axis target angular velocity based on a pre-obtained target attitude angle of the machine body and a current attitude angle of the machine body; and acquiring the current angular velocity of the body, estimating the current angular acceleration and the disturbance quantity, and acquiring the final attitude control quantity based on the target angular velocity vector. The invention regards the attitude motion as a rotation motion based on a rotation vector in a space, obtains the final attitude control quantity by estimating the current angular acceleration and disturbance quantity through the target angular velocity and the current body angular velocity, and overcomes the problem of losing the control precision. Meanwhile, a disturbance amount is introduced, so that the system has an active disturbance rejection function, and the response speed of the attitude and the adaptability of the controller are improved.
Description
Technical Field
The invention relates to the technical field of multi-rotor unmanned aerial vehicles, in particular to a multi-rotor attitude active disturbance rejection control method and system based on an axial angle vector.
Background
The current commonly used multi-rotor attitude control mode is cascade PID control, each control channel (comprising pitching, rolling and course) is independent, each control channel comprises two control loops which are an outer ring angular ring and an inner ring angular velocity ring respectively, a target attitude angle and a current actual attitude angle are input into the angular ring, a target angular velocity is generated through a PID controller, and the generated target angular velocity and the current actual angular velocity are input into the PID controller of the angular velocity ring to generate final attitude control quantity.
The PID controller has the problems of poor parameter adaptability, slow tracking response and easy overshoot, in addition, the postures of the multi-rotor aircraft are mutually coupled, and the control precision can be lost to a certain extent by independently controlling each channel.
Disclosure of Invention
The invention aims to provide a multi-rotor attitude active disturbance rejection control method and system based on an axial angle vector to solve the problem of control precision loss.
The invention solves the technical problems through the following technical means:
a multi-rotor attitude active disturbance rejection control method based on an axial angle vector comprises the following steps:
acquiring three-axis target angular velocity based on a pre-obtained target attitude angle of the machine body and a current attitude angle of the machine body;
and acquiring the current angular velocity of the body, estimating the current angular acceleration and the disturbance quantity, and acquiring the final attitude control quantity based on the target angular velocity vector.
The attitude motion is regarded as rotational motion based on a rotation vector in a space, and a final attitude control quantity is obtained by estimating the current angular acceleration and disturbance quantity through the target angular velocity and the current body angular velocity, so that the problem of losing control precision is solved. Meanwhile, a disturbance amount is introduced, so that the system has an active disturbance rejection function, and the response speed of the attitude and the adaptability of the controller are improved.
As a further scheme of the invention: the acquiring of the target angular velocities of the three axes includes:
substituting the target attitude angle of the engine body and the current attitude angle of the engine body into an Euler angle-to-quaternion formula to obtain quaternions of the target attitude angle and quaternions of the current attitude angle;
acquiring a target attitude quaternion according to the quaternion of the target attitude angle;
and acquiring an attitude error quaternion based on the quaternion of the current attitude angle and the target attitude quaternion, and calculating to obtain a target angular velocity vector.
As a further scheme of the invention: the acquiring the target attitude quaternion comprises the following steps:
based on the quaternion of the target attitude angle, a formula (1) is used for calculating a quaternion vector of a tilting error (the tilting error usually only comprises roll and pitch without course direction);
Wherein,,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
in order to obtain the target roll angle,in order to target the pitch angle,is a target course angle;
a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
the current roll angle is the current roll angle,for the purpose of the current pitch angle,is the current course angle
The target quaternion of the tilt angle (including pitch and roll) can be obtained:
acquiring a multi-rotor course target quaternion through a formula (5);
and (3) carrying out rotation motion target quaternion by using a formula (6) to obtain a limited quaternion:
according to the target quaternion of the tilting angle and the limited quaternion, finally obtaining the limited target attitude quaternion by using a formula (7);
as a further scheme of the invention:
the obtaining the attitude error quaternion comprises:
obtaining a final attitude error quaternion vector by using a formula (8);
As a further scheme of the invention: the calculating to obtain the target angular velocity vector comprises:
based on the quaternion of the attitude error, the target angular velocity vector can be obtained by using the formula (9),In order to roll the target angular velocity,in order to target the angular velocity of the pitch,is a course target angular velocity;the calculation formula of (2) is as follows:
As a further scheme of the invention: the step of acquiring the final attitude control quantity includes:
and obtaining the target angular acceleration by adopting a fast tracking function fhan, wherein the calculation formula is as follows:
whereinIn order to calculate the target angular velocity,in order to calculate the target angular acceleration,the target angular velocity calculated for equation (9), k being the kth time,in order to perform the cycle time,
wherein,are all the input of a function, and the input of the function,for tracking step lengthThe larger the tracking speed, the faster, sign is a sign function,,
According to the measured current angular speed of the bodyAnd calculating the observation angular acceleration and the observation disturbance quantity from the k moment to the k +1 moment by using a state observer, wherein the calculation formula is as follows:
whereinIn order to observe the angular velocity of the object,in order to observe the angular acceleration,in order to observe the amount of disturbance,the control quantity given to the controller is,、、and b are both adjustable parameters, and the parameters are adjustable,observing errors of the observed angular velocity and the current angular velocity;
the final control quantity can be obtained according to the target angular velocity, the angular acceleration and the current actual angular velocity and angular accelerationIs composed of
WhereinAs an error between the target angular velocity and the observed angular velocity,as an error between the target angular acceleration and the observed angular acceleration, c is a damping coefficient.
A multi-rotor attitude active disturbance rejection control system based on shaft angle vectors, comprising:
the acquisition module is used for acquiring three-axis target angular velocity based on the target attitude angle of the machine body and the current attitude angle of the machine body;
and the calculation module is used for acquiring the current angular velocity of the body, estimating the current angular acceleration and the disturbance quantity, and acquiring the final attitude control quantity based on the target angular velocity vector.
As a further scheme of the invention:
and substituting the target attitude angle of the engine body and the current attitude angle of the engine body into an Euler angle-to-quaternion formula to obtain quaternions of the target attitude angle and quaternions of the current attitude angle.
Acquiring a target attitude quaternion according to the quaternion of the target attitude angle;
and acquiring an attitude error quaternion based on the quaternion of the current attitude angle and the target attitude quaternion, and calculating to obtain a target angular velocity vector.
As a further scheme of the invention: the acquiring the target attitude quaternion comprises the following steps:
based on the quaternion of the target attitude angle, a formula (1) is used for calculating a quaternion vector of a tilting error (the tilting error usually only comprises roll and pitch without course direction);
Wherein,,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
in order to obtain the target roll angle,in order to target the pitch angle,is a target course angle;
wherein,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
the current roll angle is the current roll angle,for the purpose of the current pitch angle,is the current course angle;
the target quaternion of the tilt angle (including pitch and roll) can be obtained:
acquiring a quaternion of a multi-rotor-wing target in the direction of flight;
and (3) carrying out rotation motion target quaternion by using a formula (6) to obtain a limited quaternion:
according to the target quaternion of the tilting angle and the limited quaternion, finally obtaining the limited target attitude quaternion by using a formula (7);
as a further scheme of the invention: the obtaining the attitude error quaternion comprises:
obtaining a final attitude error quaternion vector by using a formula (8);
The invention has the advantages that:
1. the invention regards the attitude motion as a rotation motion based on a rotation vector in a space, obtains the final attitude control quantity by estimating the current angular acceleration and disturbance quantity through the target angular velocity and the current body angular velocity, and overcomes the problem of losing the control precision.
2. The invention has the active disturbance rejection function by introducing the disturbance quantity, so as to improve the response speed of the attitude and the adaptability of the controller, not only can improve the response speed and the control precision of the attitude controller of the aircraft, but also has stronger adaptability.
Drawings
Fig. 1 is a block diagram illustrating a flow of a multi-rotor attitude active disturbance rejection control method based on an axis angle vector according to the present invention.
Fig. 2 is a schematic structural diagram of a multi-rotor attitude active disturbance rejection control system based on an axis angle vector provided by the invention.
Detailed Description
In order to make the technical solutions of the present disclosure better understood by those skilled in the art, the technical solutions of the exemplary embodiments of the present disclosure will be clearly and completely described below with reference to the accompanying drawings in the exemplary embodiments of the present disclosure.
In some of the flows described in the specification and claims of this disclosure and in the above-described figures, a number of operations are included that occur in a particular order, but it should be clearly understood that these operations may be performed out of order or in parallel as they occur herein, the order of the operations being numbered such as 10, 20, etc. merely to distinguish between various operations, the order of which does not itself represent any order of performance. Additionally, the flows may include more or fewer operations, and the operations may be performed sequentially or in parallel.
It should be noted that, the descriptions of "first", "second", etc. in this document are used for distinguishing different messages, devices, modules, etc., and do not represent a sequential order, nor limit the types of "first" and "second" to be different.
Technical solutions in exemplary embodiments of the present disclosure will be described clearly and completely with reference to the accompanying drawings in the exemplary embodiments of the present disclosure, and it is apparent that the described exemplary embodiments are only a part of the embodiments of the present disclosure, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure.
Example 1
Referring to fig. 1, fig. 1 is a schematic block flow diagram of a multi-rotor attitude active disturbance rejection control method based on an axial angle vector according to embodiment 1 of the present invention, and the method is applied to a multi-rotor unmanned aerial vehicle, where the multi-rotor unmanned aerial vehicle includes three axes for flight, and the method mainly includes the following steps:
s10, acquiring three-axis target angular velocity based on the pre-obtained target attitude angle of the body and the current attitude angle of the body;
it should be noted here that the target attitude angle of the multiple rotors is、、;Representing roll in target attitude angle,Representing the pitch in the target attitude angle,Representing a heading in a target attitude angle;
the current attitude angle of the body is、、,Showing the roll in the current attitude angle of the machine body,Representing the pitch in the current attitude angle of the body,Representing the heading in the current attitude angle of the body.
It should be emphasized that the target attitude angle is obtained by the existing means, and the current attitude angle of the body is directly measured, so that the detailed description of how to obtain the target attitude angle and the current attitude angle of the body is omitted here.
Further, step S10 includes:
and S11, substituting the target attitude angle of the body and the current attitude angle of the body into an Euler angle-to-quaternion formula to obtain quaternions of the target attitude angle and quaternion of the current attitude angle.
S12, acquiring a target attitude quaternion according to the quaternion of the target attitude angle;
and S13, acquiring an attitude error quaternion based on the quaternion of the current attitude angle and the target attitude quaternion, and calculating to obtain a target angular velocity vector.
In step S11; knowing the target attitude angle (roll)And pitchCourse of the vehicle) Current attitude angle of machine body (roll)And pitchCourse of the vehicle) In order to facilitate calculation, quaternions are used for calculation instead of Euler angles, quaternions are another expression mode of attitude angles, Euler angles represent rotational motion around XYZ axes, quaternions represent rotational motion around rotation vectors in three-dimensional space, and quaternion vectors represent rotation vectorsAngle with euler、、The conversion relationship between can be expressed as:
the target attitude angle can be converted into a target quaternion according to the formula:
in order to obtain the target roll angle,in order to target the pitch angle,is the target heading angle.
The quaternion of the current attitude angle may be expressed as:
wherein,the current roll angle is the current roll angle,for the purpose of the current pitch angle,is the current heading angle.
In step S12, the method includes:
s121, calculating a vector of quaternion of tilting error (tilting error usually only comprises roll and pitch without course) by using formula (1) based on quaternion of target attitude angle;
Wherein,,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
Wherein,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
The target quaternion of the tilt angle (including pitch and roll) can be obtained:
whereinIs the attitude quaternion for the current attitude,the tilt error vector calculated for equation 1.
S121, acquiring a multi-rotor course target quaternion through a formula (5);
whereinFor the pose target quaternion vector,the target quaternion vector calculated for equation 4 contains roll and pitch only,、are elements in the course target quaternion vector.
Considering that the tilting motion is labor-saving, the rotating motion is labor-saving, and the tilting motion is the main factor for ensuring the safe flight of the airplane, therefore, the rotating motion needs to be limited to a certain extent to ensure that the tilting motion is preferential. Therefore, in the embodiment of the present application, the adjustment factor is takenAnd (3) carrying out rotation motion target quaternion by using a formula (6) to obtain a limited quaternion:
according to the target quaternion of the tilting angle and the limited quaternion, finally obtaining the limited target attitude quaternion by using a formula (7);
s13, obtaining target attitude quaternion according to the methodAnd quaternion of current attitude angleAcquiring a final attitude error quaternion vector by using a formula (8);
wherein,is the attitude quaternion for the current attitude,the constrained target attitude quaternion obtained for equation 7.ToAs elements in the attitude error quaternion vector,the sign of the error is represented by a symbol,、、are respectively Euler angles、、The error of (2).
Based on the quaternion of the attitude error, the target angular velocity vector can be obtained by using the formula (9),In order to roll the target angular velocity,in order to target the angular velocity of the pitch,is the course target angular velocity.
And S20, acquiring the current body angular velocity, estimating the current angular acceleration and disturbance quantity, and acquiring the final attitude control quantity based on the target angular velocity vector.
In performing step S20, it is necessary to convert the target angular velocity vector into a target angular velocity vector, and this conversion step is prior art and will not be described in detail.
In step S20, the method includes:
s21, firstly, obtaining a target angular acceleration by adopting a fast tracking function fhan, and calculating a formula as follows:
whereinIn order to calculate the target angular velocity,in order to calculate the target angular acceleration,the target angular velocity calculated for equation 9, k being the kth time,in order to perform the cycle time,
wherein,are all function inputs and, in particular in the present embodiment,in order to track the target(s),in order to track the derivative of the object,in order to track the step size,in order for the function to execute a cycle,the larger the tracking speed, the faster, sign is a sign function,,
S22, obtaining the current body angular velocity according to the measurementAnd calculating the observation angular acceleration and the observation disturbance quantity from the k moment to the k +1 moment by using a state observer, wherein the calculation formula is as follows:
whereinIn order to observe the angular velocity of the object,in order to observe the angular acceleration,in order to observe the amount of disturbance,the control quantity given to the controller is,、、and b are both adjustable parameters, and the parameters are adjustable,the observation error of the observed angular velocity and the current angular velocity.
The final control quantity can be obtained according to the target angular velocity, the angular acceleration and the current actual angular velocity and angular accelerationIs composed of
whereinAs an error between the target angular velocity and the observed angular velocity,and c is the error between the target angular acceleration and the observed angular acceleration, and the damping coefficient can be adjusted according to actual conditions.
Example 2
Referring to fig. 2, the present embodiment provides a multi-rotor attitude active disturbance rejection control system based on an axial angle vector, including:
the acquisition module is used for acquiring three-axis target angular velocity based on the target attitude angle of the machine body and the current attitude angle of the machine body; and is also used for:
and S11, substituting the target attitude angle of the body and the current attitude angle of the body into an Euler angle-to-quaternion formula to obtain quaternions of the target attitude angle and quaternion of the current attitude angle.
S12, acquiring a target attitude quaternion according to the quaternion of the target attitude angle;
and S13, acquiring an attitude error quaternion based on the quaternion of the current attitude angle and the target attitude quaternion, and calculating to obtain a target angular velocity vector.
In step S11; in order to facilitate calculation, quaternions are used for calculation instead of Euler angles, quaternions are another representation mode of attitude angles, Euler angles represent rotation motion around XYZ axes, quaternions represent rotation motion around rotation vectors in three-dimensional space, and quaternion vectors represent rotation motion around rotation vectors in three-dimensional spaceAngle with euler、、The conversion relationship between can be expressed as:
the target attitude angle can be converted into a target quaternion according to the formula:
in order to obtain the target roll angle,in order to target the pitch angle,is the target heading angle.
The quaternion of the current attitude angle may be expressed as:
wherein,the current roll angle is the current roll angle,for the purpose of the current pitch angle,is the current heading angle.
In step S12, the method includes:
s121, calculating a tilting error (the tilting error usually only comprises roll and pitch without course) quaternion vector by using the formula (1);
Wherein,,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
Wherein,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
The target quaternion from which the tilt angle (including pitch and roll) can be derived can be expressed as
S121, acquiring a multi-rotor-wing target quaternion in the direction of flight;
target four calculated for equation 4 containing only roll and pitchA vector of the number of elements,、are elements in the course target quaternion vector.
Considering that the tilting motion is labor-saving, the rotating motion is labor-saving, and the tilting motion is the main factor for ensuring the safe flight of the airplane, therefore, the rotating motion needs to be limited to a certain extent to ensure that the tilting motion is preferential. Therefore, in the embodiment of the present application, the adjustment factor is takenAnd (3) carrying out rotation motion target quaternion by using a formula (6) to obtain a limited quaternion:
according to the target quaternion of the tilting angle and the limited quaternion, finally obtaining the limited target attitude quaternion by using a formula (7);
s13, obtaining target attitude quaternion according to the methodAnd quaternion of current attitude angleAcquiring a final attitude error quaternion vector by using a formula (8);
is the attitude quaternion for the current attitude,the constrained target attitude quaternion obtained for equation 7.ToAs elements in the attitude error quaternion vector,the sign of the error is represented by a symbol,、、are respectively Euler angles、、The error of (2).
Based on the quaternion of the attitude error, the target angular velocity vector can be obtained by using the formula (9),In order to roll the target angular velocity,in order to target the angular velocity of the pitch,is the course target angular velocity.
And the calculation module is used for acquiring the current angular velocity of the body, estimating the current angular acceleration and the disturbance quantity, and acquiring the final attitude control quantity based on the target angular velocity vector.
When the calculation module is executed, the target angular velocity vector needs to be converted into a target angular velocity vector, and the conversion step is the prior art and will not be described in detail.
In the calculation module, comprising:
s21, firstly, obtaining a target angular acceleration by adopting a fast tracking function fhan, and calculating a formula as follows:
whereinIn order to calculate the target angular velocity,in order to calculate the target angular acceleration,the target angular velocity calculated for equation 9, k being the kth time,in order to perform the cycle time,
wherein,are all the input of a function, and the input of the function,for tracking step lengthThe larger the tracking speed, the faster, sign is a sign function,,
S22, obtaining the current body angular velocity according to the measurementAnd calculating the observation angular acceleration and the observation disturbance quantity from the k moment to the k +1 moment by using a state observer, wherein the calculation formula is as follows:
whereinIn order to observe the angular velocity of the object,in order to observe the angular acceleration,in order to observe the amount of disturbance,the control quantity given to the controller is,、、and b are both adjustable parameters, and the parameters are adjustable,the observation error of the observed angular velocity and the current angular velocity. According to the target angular velocity, angular acceleration and current realityThe final control quantity can be obtained by the angular speed and the angular accelerationIs composed of
whereinAs an error between the target angular velocity and the observed angular velocity,is a target angular acceleration
And observing the error between the angular acceleration, and c is that the damping coefficient can be adjusted according to the actual condition.
By the method, the final control quantity is finally obtainedThe adaptability is improved while the control precision is ensured.
In conclusion, the final attitude control quantity is obtained by estimating the current angular acceleration and the disturbance quantity through the target angular velocity and the current body angular velocity, the problem of losing control precision is solved, and meanwhile, the response speed of the attitude and the adaptability of the controller are improved through introducing the disturbance quantity, so that the response speed and the control precision of the aircraft attitude controller can be improved, and the aircraft attitude controller has strong adaptability.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (6)
1. A multi-rotor attitude active disturbance rejection control method based on an axial angle vector is characterized by comprising the following steps:
acquiring three-axis target angular velocity based on a pre-obtained target attitude angle of the machine body and a current attitude angle of the machine body;
acquiring the angular velocity of a current machine body, estimating the current angular acceleration and disturbance quantity, and acquiring the final attitude control quantity based on a target angular velocity vector;
the acquiring of the target angular velocities of the three axes includes:
substituting the target attitude angle of the engine body and the current attitude angle of the engine body into an Euler angle-to-quaternion formula to obtain quaternions of the target attitude angle and quaternions of the current attitude angle;
acquiring a target attitude quaternion according to the quaternion of the target attitude angle;
acquiring an attitude error quaternion based on the quaternion of the current attitude angle and the target attitude quaternion, and calculating to obtain a target angular velocity vector;
the acquiring the target attitude quaternion comprises the following steps:
calculating a tilting error quaternion vector by using a formula (1) based on the quaternion of the target attitude angle;
Wherein,,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
in order to obtain the target roll angle,in order to target the pitch angle,is a target course angle;
the current roll angle is the current roll angle,for the purpose of the current pitch angle,is the current course angle;
obtaining a tilting angle target quaternion:
acquiring a multi-rotor course target quaternion through a formula (5);
and (3) limiting the quaternion of the rotary motion target by using a formula (6) to obtain the limited quaternion:
according to the target quaternion of the tilting angle and the limited quaternion, finally obtaining the limited target attitude quaternion by using a formula (7);
3. The method of claim 2, wherein the calculating a target angular velocity vector comprises:
based on the quaternion of the attitude error, the target angular velocity vector can be obtained by using the formula (9),In order to roll the target angular velocity,in order to target the angular velocity of the pitch,is a course target angular velocity;the calculation formula of (2) is as follows:
4. The method of claim 2, wherein the step of obtaining a final attitude control variable comprises:
and obtaining the target angular acceleration by adopting a fast tracking function fhan, wherein the calculation formula is as follows:
whereinIn order to calculate the target angular velocity,in order to calculate the target angular acceleration,the target angular velocity calculated for equation (9), k being the kth time,in order to perform the cycle time,the target angular velocity at the time k +1,for the target angular velocity at the time k,is the target angular acceleration at time k +1,a target angular acceleration at time k;
wherein,are all the input of a function, and the input of the function,for tracking the step size, sign is a sign function,,
According to the measured current angular speed of the bodyAnd calculating the observation angular acceleration and the observation disturbance quantity from the k moment to the k +1 moment by using a state observer, wherein the calculation formula is as follows:
whereinIn order to observe the angular velocity of the object,in order to observe the angular acceleration,in order to observe the amount of disturbance,the control quantity given to the controller is,、、and b are both adjustable parameters, and the parameters are adjustable,to observe the observation error of the angular velocity and the current angular velocity,is the observed angular acceleration at time k +1,for the observed angular acceleration at time k,the observed disturbance amount at the time k +1,for the observed disturbance quantity at the time k,is the observed angular velocity at time k +1,is the observed angular velocity at time k;
according to the target angular velocity, the angular acceleration and the current actual angular velocityThe final control quantity can be obtained by degree and angular accelerationuIs composed of
5. A multi-rotor attitude active disturbance rejection control system based on shaft angle vectors, comprising:
the acquisition module is used for acquiring three-axis target angular velocity based on the target attitude angle of the machine body and the current attitude angle of the machine body;
the calculation module is used for acquiring the current angular velocity of the body, estimating the current angular acceleration and disturbance quantity and acquiring the final attitude control quantity based on the target angular velocity vector;
the acquiring of the target angular velocities of the three axes includes:
substituting the target attitude angle of the engine body and the current attitude angle of the engine body into an Euler angle-to-quaternion formula to obtain quaternions of the target attitude angle and quaternions of the current attitude angle;
acquiring a target attitude quaternion according to the quaternion of the target attitude angle;
acquiring an attitude error quaternion based on the quaternion of the current attitude angle and the target attitude quaternion, and calculating to obtain a target angular velocity vector;
the acquiring the target attitude quaternion comprises the following steps:
based on the purposeCalculating quaternion of the standard attitude angle by using formula (1) to calculate vector of quaternion of tilt error;
Wherein,,a vector representing the Z axis of the target attitude coordinate system in the NED coordinate system and having
in order to obtain the target roll angle,in order to target the pitch angle,is a target course angle;
wherein,a vector of Z axis of the current attitude coordinate system in NED coordinate system and having
the current roll angle is the current roll angle,for the purpose of the current pitch angle,is the current course angle;
the tilting angle target quaternion can be obtained:
acquiring a target quaternion of the rotary motion of the multiple rotors around the Z axis through a formula (5);
and (3) carrying out rotation motion target quaternion by using a formula (6) to obtain a limited quaternion:
according to the target quaternion of the tilting angle and the limited quaternion, finally obtaining the limited target attitude quaternion by using a formula (7);
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